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A 50.0resistor is connected, as in Figure to an ac generator with m=30.0V.

(a) What is the amplitude of the resulting alternating current if the frequency of the emf is 1.00kHz? (b) What is the amplitude of the resulting alternating current if the frequency of the emf is 8.00kHz?

A resistor is connected across an alternating-current generator.

Short Answer

Expert verified
  1. The amplitude of the resulting alternating current if the frequency of the emf has value f=1.00kHzis 0.600A.
  2. The amplitude of the resulting alternating current if the frequency of the emf has value f=8.00kHzis 0.600A.

Step by step solution

01

The given data

  1. Emf of the ac generator, m=30.0V
  2. Series resistanceR=50
02

Understanding the concept of resistance and Ohm’s law

Using Ohm鈥檚 law and substituting the given values of the amplitude of the ac generator and resistance of the resistor, we can find the amplitude of the alternating current. As the resistance of the circuit is independent of frequency, the current value remains the same for the same resistor.

The voltage equation from Ohm鈥檚 law,

ic=mR (i)

Here, Ris the resistance of the circuit andm the emf applied across the circuit.

03

a) Calculation of the resulting current for frequency 1.00 kHz

The amplitude of alternating current if the frequency of emf is1kHz.

Using the given data in equation (i), the current through the resistor is given as:

I=30V50I=0.600A

Hence, the value of the current is 0.600A.

04

b) Calculation of the resulting current for frequency 8.00 kHz

The amplitude of alternating current if the frequency of emf is8kHz.

The current is independent of frequency. So, it will be the same as calculated in part (a) above.

Hence, the value of the current is 0.600A.

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